Just a couple of suggestions.
First, switch the tires front to back & see what happens. You could do this one side at a time.
Second, given the age & mileage of your vehicle, I believe new shocks would not be a waste of time or money.
The Tire Rack has a very good Vibration Diagnostics chart on their site.
Printed one off a long time ago, because I HATE vibrations.
